Mathematics
An aeroplane leaves an airport and flies due North at 300 km/h. At the same time, another plane leaves the same airport and flies due West at 400 km/h. After 90 minutes, the distance between the two planes would be:
1000 km
900 km
800 km
750 km
Pythagoras Theorem
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Answer
Let aeroplane flying in north direction at 300 km/h be at point P after 1.5 hours and aeroplane flying in west direction at 400 km/h be at point Q after 1.5 hours.
Given, 90 minutes = 1.5 hours
Speed of aeroplane P = 300 km/h
As we know,
Distance traveled = Speed × Time taken
AP = 300 × 1.5 = 450 km.
Speed of aeroplane Q = 400 km/h
As we know,
Distance traveled = Speed × Time taken
AQ = 400 × 1.5 = 600 km.
From figure,
Let ∠A = 90°
By Pythagoras theorem,
Hypotenuse2 = Perpendicular2 + Base2
In triangle APQ,
⇒ PQ2 = AP2 + AQ2
⇒ PQ2 = 4502 + 6002
⇒ PQ2 = 202500 + 360000
⇒ PQ2 = 562500
⇒ PQ =
⇒ PQ = 750 km.
Hence, Option 4 is the correct option.
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